For the study, the research team wanted to determine not just when genes activate, but how their activation changes over the course of brain development. Genes activate at different points in cell development, but mapping gene development has been difficult. And past studies have focused on isolated moments in time, not on how gene expression evolves over time.
In this case, the researchers used a logistic equation (a mathematical equation useful for modeling dynamic processes) to measure when and how rapidly genes turn on and off in developing mouse brains. They found that most genes follow simple and gradual activation patterns, and that genes can be grouped into subtypes, including accelerators that speed up during late stages of development; switchers that speed up and then slow down; and decelerators that just slow down.
Researchers then developed an AI model to predict gene expression over time based on changes in nearby chromatin. The model worked well, especially for genes with a more complex regulation, and the entire procedure established the chronODE method.
They found that most genes follow predictable developmental patterns, which are dictated by their role in a cell and determine how quickly they reach maximum influence on the cell.
“In a situation where you’re treating genetic disease, you’d want to shut down the gene before it reaches its full potential, after which it’s too late,” said co-author Beatrice Borsari, who is also a postdoctoral associate in biophysics and biochemistry.
“Our equation will tell you exactly the switching point — or the point of no return after which the drug will not have the same effect on the gene’s expression,” Borsari said.
“There are many cases where it’s not just important to characterize the developmental direction you go, but also how fast you reach a certain point, and that’s what this model is allowing us to do for the first time,” added Mark Gerstein, the Albert L. Williams Professor of Biomedical Informatics at Yale School of Medicine and a professor of molecular biophysics and biochemistry, computer science, and of statistics and data science in FAS, and the study’s lead author.
Borsari and Frank underscore that the potential applications in the pharmacokinetic area are major.
Researchers called their new method “chronODE,” a name that merges the concept of time (Chronos is the god of time in Greek mythology) with the mathematical framework of ordinary differential equations (ODEs.)
“We analyze time-series biological data using the logistic ODE,” Borsari said. “In a sense, the name captures the multidisciplinary nature of our research. We work where biology meets the beauty of math. We use mathematical models to describe and predict complex biological phenomena — in our case, temporal patterns in genomic data.”
Borsari is a computational biologist with expertise in genetics and bioinformatics, while Frank is a biomedical engineer with a strong foundation in machine learning and mathematics. “Our diverse skills create a highly synergistic collaboration, and we learn a lot from each other,” Borsari said.
Other study authors include research associates Eve S. Wattenberg, Ke Xu, Susanna X. Liu, and Xuezhu Yu.